The fastest matrix multiplication algorithm
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0:00 Multiplying Matrices the standard way
2:05 The Strassen Method for 2x2 Matrices
3:52 Large matrices via induction
7:25 The history and the future
10:19 brilliant.org/TreforBazett
In this video we explore how to multiply very large matrices as computationally efficiently as possible. Then standard algorithm from linear algebra results in n^3 multiplications to multiply nxn matrices. But can we do better? The Strassen algorithm improved this to about n^2.8, first in the 2x2 case and then we can prove via induction it works in general. This improvement has seen a range of improvements over the last 50 years inching closer - but still far away - to the theoretically limit of n^2.
Further Reading:
Going into the details of the laser method (what happened after the Strassen algorithm I showed): https://theoryofcomputing.org/article...
The AlphaTensor AI paper: https://www.nature.com/articles/s4158...
A nice summary from Quanta: https://www.quantamagazine.org/mathem...
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